For societal applications, the sensitive variable is defined following regulations as presented in Section REF . The variable \(A\)  is known since it is chosen by the regulator, and hence, is either directly available in the data or proxies can be found to estimate it. The main difficulty when working with high dimensional inputs such as images (but also natural language data, time series or graphs) is that the bias may not be explicitly present in a particular input dimension or variable, but is rather hidden in a latent representation of the input data. For instance, an image-based classifier would not naturally have a different rate of positive decisions for males and females because of the intensity of a specific pixel. It would instead detect specific patterns or features in the input images and potentially use this information, leading to unfair decisions with respect to a gender sensitive variable. As discussed in Section , neural network classifiers or regressors change by construction the representation of the input data into a lower dimensional latent (or feature) space before making their predictions based on this latent information. Illustrations of how a network can project the input information in a latent space can be found in the VGG and ResNet papers [1]}, [2]}. It would then be tempting to believe that the hidden variables explaining the undesirable biases would be found in the latent space but this is not necessarily the case. This information can still be distilled in different latent variables unless a specific process is made to isolate it [3]}. Hence, bias detection is an essential, potentially arduous task when dealing with images.
